z-logo
open-access-imgOpen Access
Graph Realizations Constrained by Connected Local Dimensions and Connected Local Bases
Author(s) -
Varanoot Khemmani,
Witsarut Pho-on,
Supachoke Isariyapalakul
Publication year - 2022
Publication title -
wseas transactions on mathematics
Language(s) - English
Resource type - Journals
eISSN - 2224-2880
pISSN - 1109-2769
DOI - 10.37394/23206.2022.21.1
Subject(s) - combinatorics , connectivity , vertex connectivity , mathematics , vertex (graph theory) , connected component , graph , simply connected space , basis (linear algebra) , strongly connected component , cardinality (data modeling) , discrete mathematics , computer science , geometry , data mining
For an ordered set W = {w1,w2, ...,wk} of k distinct vertices in a connected graph G, the representation of a vertex v of G with respect to W is the k-vector r(v|W) = (d(v,w1), d(v,w2), ..., d(v,wk)), where d(v,wi) is the distance from v to wi for 1 ≤ i ≤ k. The setW is called a connected local resolving set of G if the representations of every two adjacent vertices of G with respect to W are distinct and the subgraph ⟨W⟩ induced by W is connected. A connected local resolving set of G of minimum cardinality is a connected local basis of G. The connected local dimension cld(G) of G is the cardinality of a connected local basis of G. In this paper, the connected local dimensions of some well-known graphs are determined. We study the relationship between connected local bases and local bases in a connected graph, and also present some realization results.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.
Having issues? You can contact us here